Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Definite Integration

NDA 2010 · Mathematics · Definite Integration

What is the value of ∫_1^2 e^x((1)/(x)-(1)/(x^2)) d x

What is the value of ∫12ex(1x−1x2)dx\int_1^2 e^x\left(\frac{1}{x}-\frac{1}{x^2}\right) d x

Options

  1. Ae(e2−1)e \left(\frac{e}{2}-1\right)
  2. Be(e−1)e(e-1)
  3. Ce−1ee-\frac{1}{e}
  4. D0

Correct answer

A. e(e2−1)e \left(\frac{e}{2}-1\right)

Step-by-step solution

∫12(exx−exx2)dx=∫12exxdx−∫12exx2dx=[1x⋅ex]12−∫12−1x2⋅exdx−∫12exx2dx=12e2−e1=e(e2−1)\begin{aligned} & \int_1^2\left(\frac{e^x}{x}-\frac{e^x}{x^2}\right) d x \\ & =\int_1^2 \frac{e^x}{x} d x-\int_1^2 \frac{e^x}{x^2} d x \\ & =\left[\frac{1}{x} \cdot e^x\right]_1^2-\int_1^2-\frac{1}{x^2} \cdot e^x d x-\int_1^2 \frac{e^x}{x^2} d x \\ & =\frac{1}{2} e^2-e^1=e\left(\frac{e}{2}-1\right)\end{aligned}
Practice Definite Integration on Quantrex Academy →

More from Definite Integration

Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ∫_0^4(f(x))/(g(x))\,dx… NDA 2026Passage: Let ∫_0^ (π)/(2) (a x+b x)/((a+b)( x+ x))\,dx=k . Question: What is the value of… NDA 2026Passage: Let f(x)= x and g(x)-f(x)=f(4-x) . Question: What is ∫_0^4(f(4-x))/(g(4-x))\,dx… NDA 2026Passage: Let ∫_0^ (π)/(2) (a x+b x)/((a+b)( x+ x))\,dx=k . Question: What is ∫_0^ (π)/(2)… NDA 2026Consider the following for the two (02) items that follow: Let f(x) = [x^2] , where [·]… NDA 2025What is ∫_n^ n+1 (x - [x])\, dx , where [·] is the greatest integer function and n is a… NDA 2025If I_1 = ∫_e^ e^2 (dx)/( x) and I_2 = ∫_1^2 (e^x)/(x)\, dx , then which one of the… NDA 2025Paragraph: Let I=∫_0^ (π)/(2) (f(x))/(g(x)) d x , where f(x)= x and g(x)= x+ x+1 .… NDA 2024Paragraph: Let f(t)= (t+ 1+t^2 ) and g(t)= (f(t)) . Question: What is ∫_ -π ^π g(t) d t… NDA 2024Paragraph: Let f(x)=|x^2-x-2| Question: What is ∫_0^2 f(x) d x equal to? NDA 2024What is ∫_ -1 ^1(3 x- 3 x) ^2 x d x equal to? NDA 2024What is ∫_0^ (π)/(2) (a+ x)/(2 a+ x+ x) d x equal to? NDA 2024Let p=∫_a^b f(x) d x and q=∫_a^b|f(x)| d x . If f(x)=e^ -x , then which one of the… NDA 2024Let f(x)=|x-1|, g(x)=[x] and h(x)=f(x) g(x) where [.] is greatest integer function. What… NDA 2024Let f(x)=|x-1|, g(x)=[x] and h(x)=f(x) g(x) where [.] is greatest integer function. What… NDA 2024Let 3 f(x)+f((1)/(x))=(1)/(x)+1 What is 8 ∫_1^2 f(x) d x equal to? NDA 2024 Full Definite Integration list Definite Integration JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs